Critical Evaluation and Thermodynamic Optimization of Calcium Magnesium Manganese Oxygen System

Transcription

1 Critical Evaluation and Thermodynamic Optimization of Calcium Magnesium Manganese Oxygen System SOURAV KUMAR PANDA Department of Mining and Materials Engineering McGill University, Montreal JULY 2013 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Science Sourav Kumar Panda,

2 Acknowledgements I would like to express my sincere gratitude towards my supervisor Prof. In-Ho Jung, whose continuous guidance and financial assistance was indispensable throughout my study. I am very grateful to my family who constantly encouraged me in fulfillment of my thesis. I would like to thank Dr. Pierre Hudon, for their helpful advice during the course of my study. I am grateful to all my research group mates in High-temperature Thermochemistry Group for their constructive comments. I would like to acknowledge the financial assistance provided by JFE Steel Corporation, POSCO, TATA Europe, Nippon Steel Corporation, RIST Korea, Nucor Steel, Sumitomo Metals, Hyundai Steel, QIT, Voestalpine, RHI and NSERC for my research work. I am also thankful to my friends Saikat, Manas, Bikram, Sazol, Dmitri, Sriraman, Dong-geun and Junghwan for their enthusiastic support throughout my study at McGill University. 1

3 Abstract The prediction of thermodynamic properties and phase equilibria of an oxide system can plays an important role in the development and understanding of metal1urgical, ceramic and geological processes. The thermodynamic databases, developed by a critical evaluation and optimization of all existing thermodynamic properties and phase diagram, can help in understanding the reaction mechanism in various industrial processes more clearly and in developing new technology for various industries. As part of a large thermodynamic database development for steelmaking applications, all solid and liquid phases of Ca-Mg-Mn-O system were critically evaluated and optimized in the present study. The optimization of all systems in this study is self-consistent with thermodynamic principles. All the binary and ternary system have been critically evaluated and optimized based upon available phase-equilibrium and thermodynamic data. All thermodynamic models for each solutions used in this study were developed on the basis of their structure. In this way, the configurational entropy of solution can be taken into account properly in the Gibbs energy of solution. The molten oxide was modeled by the Modified Quasichemical Model, which takes into account short-range ordering of second-nearest-neighbor cations in the ionic melt. Extensive solid solutions such as spinel were modeled within the framework of the Compound Energy Formalism with consideration of their complex sublattice crystal structures. Other solid solutions such as monoxide were modeled using random mixing of ions on cation sites using a polynomial expansion of the excess Gibbs energy. All the thermodynamic calculations in the present study were carried out using FactSage TM thermodynamic software. 2

4 RÉSUMÉ La prédiction des propriétés thermodynamiques et des équilibres de phases d'un système d'oxydes peut jouer un rôle important dans le développement et la compréhension de processus metal1urgiques, céramiques et géologiques. Les bases de données thermodynamiques, mises au point par une évaluation critique et l'optimisation de toutes les propriétés thermodynamiques et diagrammes de phase existants, peut aider à comprendre plus clairement les mécanismes de réaction impliqués dans plusieurs procédés industriels et aider à développer de nouvelles technologies pour diverses industries. Dans le cadre du développement d une grande base de données thermodynamiques pour des applications sidérurgiques, toutes les phases solides et liquides du système Ca-Mg-Mn-O ont été évaluées de façon critique et optimisées dans la présente étude. L'optimisation de tous les systèmes est en accord avec les principes thermodynamiques. Tous les systèmes binaires et ternaires ont été évalués de façon critique et optimisés en utilisant toutes les données thermodynamiques et d équilibre de phase disponibles. Tous les modèles thermodynamiques employés pour chacune des solutions utilisées dans cette étude ont été élaborées sur la base de leur structure. De cette façon, l'entropie de configuration de la solution peut être correctement prise en compte dans l'énergie de Gibbs. La phase liquide fut modélisée avec le Modèle Quasichimique Modifié qui tient en compte dans le liquide de la mise en ordre locale des cations qui sont les deuxièmes voisins les plus proches. Des solutions solides, telles que le spinelle, ont été modélisés avec le Formalisme de l Énergie des Composés en tenant compte de la structure cristalline complexe de leur sous-réseau. D autres solutions solides telles que le monoxyde ont été modélisés en utilisant un mélange aléatoire des ions sur les sites cationiques et un polynôme pour l énergie de Gibbs. Tous les calculs thermodynamiques de la présente étude ont été réalisés en utilisant le logiciel thermodynamique FactSage TM. 3

5 Table of Contents 1. Introduction Motivation of research Objective Thermodynamic modeling CALPHAD Thermodynamic models Liquid solutions Structure Modified Quasichemical Model Extension to a ternary system from a binary system Solid Solutions Monoxide Solution Regular solution model Spinel solution Structure Compound Energy Formalism References Method of Operation Critical evaluation and thermodynamic modeling of Mg-Mn-O system Introduction Phases and thermodynamic models

6 Molten oxide Monoxide solution Spinel: cubic and tetragonal Cubic spinel Tetragonal spinel Stoichiometric compounds Metallic Phases Critical evaluation/optimization of experimental data MgO-MnO system MgO-MnO-Mn 2 O 3 system MgMn 2 O 4 cubic spinel Phase diagram Conclusion References Figures Critical thermodynamic evaluation and optimization of Ca-Mg-Mn-O system Introduction Phases and thermodynamic models Molten oxide Monoxide solution Stoichiometric spinel-camn 2 O

7 Stoichiometric compounds Critical evaluation/optimization of experimental data Thermodynamic data Phase diagram data Phase diagram data at air Phase diagram at pure oxygen Ca-Mg-Mn-O System: Under Reducing Conditions Conclusion References Figures Conclusions

8 List of Figures Figure 2.1 Schematic representation of the structure of sodium silicate glass by 15 Warren and Biscoe [3] Figure 2.2 Some geometric models used for estimating ternary thermodynamic 20 properties from the optimized binary data (reproduced from Pelton [4]). Figure 2.3 Schematic representation of a NaCl crystal structure 22 Figure 2.4 Structure of a unit cell of spinel AB 2 O 4 24 Figure 2.5 The variation of cation distribution of MgAl 2 O 4. The inversion parameter 25 is defined as the mole fraction of Al 3+ on tetrahedral sites. [6] Figure 4.1 Calculated phase diagram of the Mg-Mn-O at 1000 C and 1 bar total 48 pressure. Solid lines are the phase boundaries. Figure 4.2 Activity of MgO and MnO in the MgO-MnO monoxide solution Figure 4.3 Enthalpy of mixing of MgO-MnO monoxide solution 49 Figure 4.4 Optimized phase diagram for MgO-MnO system 50 Figure 4.5 Calculated cation distribution in MgMn 2 O 4 spinel 50 Figure 4.6 Calculated phase diagram of Mg-Mn-O at air with experimental data. (a) 51 comparison with experimental data of Riboud et al. [36] and Ghozza et al. [38], and (b) comparison with experimental data of Barkhatov et al. [39], Silva [40], Wartenberg and Prophet [41] and Oliviera and Brett [42]. Here, C-Sp and T-Sp denotes cubic spinel and tetragonal spinel respectively. Figure 4.7 Figure 4.7: Calculated MgO-MnO-Mn 2 O 3 ternary phase diagram in air with experimental data of Oliviera and Brett [42]. Here, C-Sp and Mono denotes cubic spinel and monoxide, respectively. 52 Figure 4.8 Figure 4.8: Calculated partial pressure ( ) - composition diagram for Mg-Mn-O system along with experimental data by Golikov et al. [43]: (a) 800 C (b) 900 C (c) 1000 C. Here, C-Sp and T-Sp denotes cubic spinel and tetragonal spinel respectively. Figure 5.1 Calculated CaO-MgO phase diagram by Wu et al. [1] 69 Figure 5.2 Calculated CaO-MnO phase diagram by Wu et al. [1] 69 7

9 Figure 5.3 Calculated MgO-MnO phase diagram in the previous chapter [2] 70 Figure 5.4 Calculated heat capacity of CaMnO 3 along with the experimental data 70 [14, 16-18] Figure 5.5 Calculated heat capacity of CaMn 2 O 4 along with the experimental data 71 [20] Figure 5.6 Calculated heat capacity of CaMn 7 O 12 along with the experimental data [21,22] 71 Figure 5.7 Optimized phase diagram of CaO-Mn 2 O 3 at air compared with 72 experimental data (a) compared with experimental data of Riboud and Muan[10] and Toussaint[25], (b) compared with experimental data of Horowitz and Longo [23] and Tanida and Kitamura [24]. Here, C-Sp and T-Sp denotes cubic spinel and tetragonal spinel respectively. Figure 5.8 Optimized phase diagram of CaO-Mn 2 O 3 at p O2 1 atm compared with 73 Figure 5.9 experimental data from Horowitz and Longo [23]. Here, C-Sp and T-Sp denotes cubic spinel and tetragonal spinel respectively. Optimized CaO-MgO-MnO phase diagram showing isothermal line at 1500⁰C at 10-9 atm along with the experimental data from Woermann and Muan [26] 73 8

10 List of Tables Table 4.1 Optimized model parameters of solutions in the MgO-MnO-Mn 2 O 3 system Table 5.1 Already optimized model parameters for CaO-MgO [1], CaO-MnO [1] and MgO-MnO[2] Table 5.2 Optimized model parameters of solutions in the CaO-Mn 2 O 3 system 61 9

11 List of Symbols C p Molar Heat Capacity (J/mol.K) Standard Gibbs energy of i Gibbs energy of solution Exess Gibbs energy in solution Molar excess Gibbs energy in Solution Molar Gibbs energy of i Gibbs energy change for the formation of two moles of i-j pairs Standard enthalpy of i Molar enthalpy of mixing Enthalpy of formation of the compound from the elements Number of moles of i-j bonds in one mole of the solution Excess interaction parameter between A and B T wt.% yi Yi Xi Xij Zi Standard entropy of component i Entropy of formation of the compound from the elements Molar configurational entropy of solution Molar non-configurational entropy of solution Number of moles of component i Absolute temperature (K) Weight percent Site fraction of component i Coordination-equivalent fractions Mole fraction of component i in solution Pair fraction of i-j pairs Coordination number of i The value of Zi when all the nearest neighbors of an i are i s The value of Zi when all the nearest neighbors of an i are j s 10

12 1. Introduction 1.1. Motivation of research The Ca-Mg-Mn-O system is important in the ceramics and metallurgical industries, particularly for its role in many refractories. Despite its importance, the phase equilibria in this system have not been well studied. Experimental study of the system is complicated by the strong dependence of the equilibria on the oxygen pressure and by the high melting temperature of the spinel phase. Therefore, critical assessment of the data is required in order to understand and model this system more accurately. 1.2 Research objective The main goal of the present study is to perform a critical assessment and optimization of the thermodynamic properties and phase equilibria of MgO-MnO-Mn 2 O 3 (Mg-Mn-O) system and CaO-MnO-Mn 2 O 3 (Ca-Mn-O) system. In the thermodynamic optimization of a chemical system, all available thermodynamic and phase equilibrium data are evaluated simultaneously in order to obtain one set of model equation for the Gibbs energies of all phases as functions of temperature and composition. From these equations, all of the thermodynamic properties and phase diagram can be back calculated. In this way, all the data are rendered self-consistent and consistent with thermodynamic principles. Thermodynamic property data, such as activity data, can aid in the evaluation of the phase diagram and phase diagram measurements can be used to deduce thermodynamic properties. Discrepancies in the available data can be often being resolved, and interpolations and extrapolations can be made in a thermodynamically correct manner. The following are the objective of my thesis: Thermodynamic Optimization of Mg-Mn-O phase diagram In the present study, the thermodynamic properties of the Mg-Mn-O system were optimized on the basis of the previously optimized Mn-O and MgO-MnO system. The present optimization covers the range from reduce oxygen pressure to air pressure and temperature from 25 C to liquidus Thermodynamic Optimization of Ca-Mn-O phase diagram 11

13 The thermodynamic properties of the Ca-Mn-O system were also optimized on the basis of the previously optimized Mn-O and CaO-MnO system. The present optimization covers the range of oxygen partial pressures from equilibrations with pure oxygen to air pressure and temperature from 25 C to liquidus. 2. Thermodynamic modeling 2.1. CALPHAD CALPHAD is a acronym for CALculations of PHAse Diagrams. It is better described as: The Computer Coupling of Phase Diagrams and Thermochemistry. Kattner in 1997 described phase diagram as visual representation of the state of a material as a function of temperature, pressure and concentration of the constituent components. It is a basic tool which helps us in understanding phase equilibria for higher order systems. Pelton and Schmalzried(Pelton and Schmalzried, 1973) defined a phase diagram as the geometric representation of the loci of the thermodynamic parameters when equilibrium among phases under a specified set of conditions is established. However, not much experimental work has been done for predicting the phase diagram for multicomponent system. So, in order understand the phase equilibria and thermodynamic properties of the multicomponent systems, construction of multicomponent thermodynamic database started in late 1960 s. In this technique, all types of thermodynamic data such as phase diagrams, phase equilibria and activity etc. are critically evaluated and optimized simultaneously, using proper thermodynamic models, in order to construct a database for multicomponent system. At present, there are numerous research groups which are using CALPHAD technique for preparation of multicomponent database. Some of the well-established groups are Thermo-Calc group (Thermo-Calc, 2002) at KTH in Sweden, the THERMODATA group (THERMODATA, 2002) in France, Thermotech Inc. (Thermotech, 2002) in the UK, and the thermochemical group at NIST (NIST, 2002) in the USA, the FACT group (FactSage, 2002) at Ecole Polytechnique in Canada, the MTDATA group (MTDATA, 2002) at NPL in the UK and the IRSID GROUP in France. Moreover, Scientific Group Thermodata Europe (SGTE, 2002) is a consortium of research groups formed to accelerate the development of alloy database. The thermochemical 12

14 software s and multicomponent database developed by these groups are of immense help in understanding and interpreting the phase equilibria in high order systems which can be applied in academics and industries Thermodynamic models Thermodynamic models are essential to appropriately represent the thermodynamic properties of any materials. For proper representation of the thermochemical properties of a complex solution, we require a sophisticated and refined model. For this, all the models which are used are based on the structure of the solution to adequately represent the configurational entropy of the solution. Also these models have high predictive capability in higher-order systems. A good model should be able to represent the thermodynamic properties with just a small numbers of adjustable parameters. Hence, models have been developed which can describe the configurational entropy of the solutions without the addition of large arbitrary model parameters. Basic Equations Pure compounds The standard Gibbs energy of a pure substance i is written as: G i o H i o - TS i o (2.1) where are respectively the standard Gibbs energy, enthalpy and entropy of substance i, and T is the absolute temperature. For solutions Bragg-Williams random mixing solution: When two components A and B are mixed then the Gibbs energy of the solution depends upon the interaction between the A and B atoms or molecules. The Gibbs energy of a solution in which there is no interaction between A and B is an ideal solution for which: g m g o A n A g o n - T S conf where is the molar Gibbs energy of the solution, is the molar Gibbs energy of component i, and is configurational entropy obtained by randomly mixing moles of A and moles of B on the same sublattice. It can be written as: S conf -RT ( n A ln A n ln ) (2.3) 13 (2.2)

15 However all solutions do have interactions among the atoms mixing to form a solution. Such interactions can be called energy of the solution is given by:, the molar excess Gibbs energy of the solution. In that case the g m g o A n A g o n - T S conf g (2.4) can expanded as a polynomial in the mole fractions as: q i A i A (2.5) where i A are the more fractions of i and and the excess interaction parameters ( = a + bt + ct 2. ) are the model parameters. If only is used to describe the thermodynamic properties of a solution, it is known as a regular solution. If q i A parameter is temperature dependent, then the S non-config term is non-zero. Development of a model In many cases, the thermodynamic properties of a binary solution can be described using the above expression. Problem arises, when such an expression is used to predict the thermodynamic properties of higher order system from the model parameters of the low-order sub-systems. Sometimes a large number of temperature- and composition-dependent excess model parameters are needed in order to represent all the thermodynamic properties of a binary system as well as higher order system. This results in non-configurational entropy terms of the model to be large and decreases predictive ability of the model for higher order system. Therefore, during development of a model, one of the most important factors is how well the configurational entropy of the solution is described without the addition of large arbitrary model parameters. That is, during modeling the real structure of the solution must be taken into account in the model. In the present study, solution phases such as liquid slag, spinel and monoxide are described using different thermodynamic models which are based on real solution structures Liquid solutions (slag) The liquid phase is technologically one of the most important phases appearing in every system. The adequate representation of its Gibbs energy plays an important role in database preparation for multicomponent alloys. Therefore, to adequately represent the thermodynamic properties of 14

16 the liquid phase, Pelton and Blander [1] and more recently by Pelton et al. [2] developed the Modified Quasichemical Model (MQM). In this, they modified the classical quasichemical model by expressing the energy of pair formation as a polynomial in the pair formation rather than the component functions Structure One of the very examples of a liquid solution is a sodium silicate glass [3]. In this, the silicon atoms are surrounded by 4 oxygen atoms which hare arranged in the form of tetrahedron. The Si and O atoms form SiO 4 tetrahedra which are joined together in chains or rings by bridging atoms (BO). Cations such as Na +, Fe 2+, Mn 2+, Ca 2+, etc. tend to break these BO and form non-bridging oxygen s, O -, or free oxygen ions, O 2-. These silicate melt contains various 3 dimensional interconnected anion units such as SiO 2, Si 2 O 2-5, Si 2 O , Si 2 O 7 and SiO 2-4. The degree of depolymerisation of a silicate melt is often expressed by the ratio (NBO/T), where T is the number of tetrahedrally coordinated atoms such as Si. This ratio (NBO/T) affects the physical properties of the silicate melts such as thermal conductivity, viscosity etc. Figure 2.1 shows the schematic structure of silicate melts. Figure 2.1: Schematic representation of the structure of sodium silicate glass by Warren and Biscoe [3] 15

17 Modified Quasichemical Model The modified quasichemical model [1-2], which takes into account short-range ordering of second-nearest-neighbor cations in the ionic melt, is used for modeling the slag (molten oxide). For example, for the MgO-MnO-MnO 1.5 slag these reactions are: (A A ) + ( B B ) = 2( A B ); (2.6) Where (i j) represents a first nearest-neighbour pair. is the nonconfigurational Gibbs energy change for the formation of two moles of (A-B) pairs. Let and be the number of moles of A and B, be the number of moles of (i j) pairs, and Z A and Z B be the coordination numbers of A and B. The pair fractions, mole fractions, and coordination-equivalent fractions are defined respectively as: (2.7) A n A (n A n ) 1- (2.8) A An A ( A n A n ) A A ( A A ) 1 (2.9) The following equations may also be written as follows by mass balance: (2.10) (2.11) where represents total number of bonds emanating from an i atom, ions or molecules. In coordination equivalent fractions defined in equation (2.11), is the total number of pairs in one mole of a solution. If be the fraction of i- pairs in solution, equation (2.10) and (2.11) can be written as (2.12) 16

18 (2.13) The molar enthalpy and excess entropy of mixing are assumed to be directly related to the number of A-B pairs: (2.14) The gibbs energy of the solution can be written as: ( ) (2.15) (2.16) where and are the molar Gibbs energies of the pure component and is the configurational entropy of mixing of random distribution of the (A A), (B B) and (A B) pairs in the one dimensional Ising approximation: is expanded in terms of the pair fractions: [ ( ) ( ) ( ) ] (2.17) (2.18) where, and are the parameters of the model which may be functions of temperature. The equilibrium pair distribution is calculated by minimizing with respect to at constant composition. (2.19) This gives the equilibrium constant for the quasichemical reaction of ( q.1): ( ) ( ) (2.20) 17

19 When ( ) = 0, the solution of the equation (2.9), (2.12) and (2.13) gives a random distribution with, and, and equation (2.17) reduces to ideal Roultian entropy of mixing. When ) becomes progressively more negative, the reaction (Eq. 1) is shifted progressively to the right, resulting in the plot of versus composition to become V-shaped and that of versus composition to become m-shaped with minima at. When becomes postitve, (A-A) and (B-B) pairs dominate. Therefore, the Quasichemical model can also treat such clustering which accompanies positive deviation from ideality. Usually, the parameter is expanded as a polynomial term of equivalent fractions. At maximum SRO, the composition is determined by the ratio of the coordination numbers Z B / Z A as given by the following equations: ( ) ( ) (2.21) ( ) ( ) (2.22) where and are the values of respectively when all the nearest neighbors of an A are A s, and when all nearest neighbors of an A are s, and where defined similarly. (Note: and represent the same quantity and can be used interchangeably.) This model is sensitive to the ratio of the coordination numbers and less sensitive to their absolute values. The use of the one-dimensional Ising model in equation (2.17) introduces a mathematical approximation into the model which can be partially compensated by selecting values of Z B and Z A which are smaller than the actual values Extension to a ternary system from binary system Several geometric models have been proposed to estimate the excess Gibbs energy of a ternary system from optimized binary model parameters. Pelton [4] model presented a detail description of these models which are illustrated in Figure 3. The selection geometric models depends upon the nature of each binary system whose model parameters are interpolated to the ternary system. 18

20 In all these models the excess Gibbs energy ( i i ) of a solution at any composition p can be estimated from the binary interaction parameter or the excess Gibbs energies of the binary sub-system at points a, b and c. The excess Gibbs energy when the solution is modeled using the MQM is: s (2.23) where is the Gibbs energy change for the reaction: i i i ) (2.24) If ternary data is available, ternary terms can be used to estimate the ternary interactions. However, precautions are taken to keep these terms as small as possible, otherwise doubts is cast upon the predictive ability of the model. These ternary polynomial terms are identically zero in the three binary sub-systems. The Kohler and Muggianu models [4] in Figure 2.2 are symmetric models, whereas the Kohler/Toop and Muggianu/Toop models in Figure 2.2 are asymmetric models as one component is singled out. If component 2 and 3 are chemically similar while component 1 is chemically different, then asymmetric model is more physically reasonable than symmetric model. A symmetric model and an asymmetric model will give very different results, when is large and depends strongly upon composition. Pelton [4] showed that if the models are used improperly then it can lead to thermodynamically inconsistent and unjustifiable results. 19

21 Figure 2.2: Some geometric models used for estimating ternary thermodynamic properties from the optimized binary data (reproduced from Pelton [4]). Chartrand and Pelton [5] gave a detailed description of the estimation of the excess Gibbs energies in a ternary solution from binary model parameters when liquid phase is modeled by MQM. If the three binary subsystems of a ternary system have been optimized and the parameters are in the form of Equation 2.18 and symmetric Kohler-type approximation is chosen for the 1-2 subsystem, then can be written: ( ) ( ) (2.25) 20

22 If Toop-type approximation is chosen, then can be written as: (2.26) To estimate the Gibbs energy of ternary or multicomponent solutions from the optimized lowerorder parameters, FactSage TM thermodynamic software [6] allows users to use any of these geometric models which increase the flexibility and the ability to find out the Gibbs energy Solid Solutions Thermodynamic modeling of solids includes stoichiometric compounds, terminal solid solution or stoichiometric compounds with wide range of homogeneity. Sometimes some compounds have such a large homogeneity range that they are called with specific names such as spinel solid solution. For any stoichiometric phase A x B y per mole of atoms is represented as: (2.27) where and are the enthalpy of formation of the compound from the states i and j of elements A and B respectively Monoxide solutions Monoxide solid solution has a space group Fd3m which are MO based oxides where M 2+ is a divalent cation such as Mg, Ca, Fe 2+, Mn 2+, Co 2+, Ni 2+, etc. Almost all monoxide shows complete solid solution except CaO-MgO system, which exhibits limited mutual solubility s. Some of the N2O3 type solid oxides get dissolved in the monoxide solution where N is a trivalent cation such as Al 3+, Cr 3+ and Fe 3+. Monoxide solution has a structure similar to that of NaCl (halite), therefore known as halite (rock salt) solution (Figure 2.3). In a monoxide solid solution, when two MO oxides mix, the mixing usually occurs between the cations in the cation sites. Based on this, the following model is being used to model the monoxide solutions. 21

23 Figure 2.3: Schematic representation of a NaCl crystal structure Regular solution model Regular solution model is used to model terminal solid solutions or monoxide solutions which appeared in binary systems. In this, the model assumes random mixing of the atoms on one sub lattice while the other lattice is fixed, one randomly replacing the other by substitution on lattice sites. The Gibbs energy of such a solution in which atoms A and B replace each other on one lattice sites is given as: [ ] (2.28) The phases which exhibit homogeneity in two or more sublattices are modeled using sublattice models. The sublattice model with random mixing on each sublattice in its most general form is called as Compound Energy Formalism. 22

24 Spinel solution Structure Most of the spinel compounds belong to the space group Fd3m. Figure 2.4 shows the schematic structure of spinel. It has a general formula AB 2 O 4. In one unit cell of AB 2 O 4 shown in Figure1, A atoms are located in the 8 tetrahedral positions (represented by green circles), B atoms are in the 16 octahedral positions (represented by red circles) and oxygen atoms in the 32 positions ( represented by blue circle). One unit cell contains 32 oxygen atoms, so, there are eight AB 2 O 4 formula units. The lattice parameter in oxide spinel is approximately nm. A simple spinel contains two different cations in the ratio of 2:1. Theoretically, all spinels may be classified into three classes, normal, inverse and mixed. A normal spinel is one in which all the (A) cations reside in the tetrahedral site all the (B) cations reside in the octahedral sites. A fully inverse spinel is a one in which the (B) cations are evenly split between tetrahedral and octahedral site and all the (A) cations are reside in the octahedral sites. All real spinels generally fall in the category of mixed spinels, i.e. both the cations (A) and ( ) are present in both tetrahedral and octahedral sites. All the well-known oxide spinels are thermodynamically very stable at 1 bar total pressure. For example: MgAl 2 O 4 (spinel), Fe 3 O 4 (magnetite), FeAl 2 O 4 (hercynite), MgFe 2 O 4 (magnesium ferrite), MgCr 2 O 4 ( magnesium chromite), FeCr 2 O 4 ( iron chromite), MnAl 2 O 4 (galaxite), CoAl 2 O 4, NiAl 2 O 4 etc. However, some silicate spinels, Mg 2 SiO 4, Fe 2 SiO 4, Co 2 SiO 4 and Ni 2 SiO 4 are stable under high pressure because the olivine structure (A 2 SiO 4 ) transforms to the spinel structure at high pressure. Oxide spinels can dissolves γ-a 2 O 3 type oxides e.g. γ-al 2 O 3, γ-fe 2 O 3, γ-cr 2 O 3, etc. This results in introduction of vacancies on octahedral sites which eventually leads to wide ranges of solid solution. 23

25 Figure 2.4: Structure of a unit cell of spinel AB 2 O 4 The spinel structure has unique characteristics of cation distributions (order/disorder). The cation distribution of a spinel varies with temperature. The usual way of determining cation distribution is to quench the sample at one particular temperature and do crystallography measurements. But, the distribution of cation within tetrahedral and octahedral sites is unquenchable above a certain temperature because after that temperature the ordering-disordering process is too fast to be quenched. That temperature is known as unquenchable temperature, T unquen. In this case, in-situ measurements are the only solution. On the other hand, the spinel does not reach an equilibrium distribution of cations within two sites below a certain temperature because below that temperature the ordering-disordering process is too slow and does not reach equilibrium. That temperature is known as frozen temperature, T froz. In case of MgAl 2 O 4, Jung et al. [7] did 24

26 thermodynamic optimization of MgAl 2 O 4 cubic spinel and found out the frozen and unquenchable temperature to be approximately 700 C and 923 C, respectively (Figure 2.5). Figure 2.5: The variation of cation distribution of MgAl 2 O 4. The inversion parameter is defined as the mole fraction of Al 3+ on tetrahedral sites. [7] Compound Energy Formalism For modelling a spinel, a two-sublattice model by Degterov et al. [8] in the framework of the Compound Energy Formalism (CEF) by Hillert et al. [9] is used for describing the Gibbs energy of spinel solutions. The Gibbs energy of the spinel solution is expressed, in the CEF, as (2.29) where and represent the site fractions of constituents i and j on the tetrahedral and the octahedral sublattices, respectively; is the Gibbs energy of n end member [i] T [j] O 2 O 4 in which T (tetrahedral site) and O (octahedral site) sites are occupied only by i and j cations, respectively; is the configurational entropy which takes into account random mixing on each sublattice: 25

27 i ( i i i ) (2.30) and is the excess Gibbs energy: (2.31) where parameters is the interaction energies between cations i and j on the first sublattice when the second sublattice is occupied only by k cations and similarly the parameters is the interaction energies between cations i and j on second sublattice when the first sublattice is occupied only by k cations. The interaction energies, and are internally set in the model as follows:.. (2.32).. (2.33) The interaction between i and on a sublattice is assumed to be the same, independent of which cation resides on the other sublattice. The interaction energies can be expressed by Redlich-Kister a power series expansion (Redlich and Kister [10] and Pelton and Bale [11]) which depends upon the composition: ( ) (2.34) ( ) (2.35) Gibbs energies G ij of end-members of the model are formed by taking i from tetrahedral sublattice and from octahedral sublattice. These are the primary model parameters. However, it is not possible to determine from the experimental data alone the Gibbs energies of all endmembers. For fixing the values of these Gibbs energies properly, certain logical and physically 26

28 meaningful assumptions should be made. In the present model, physically meaningful linear combinations of the end-members Gibbs energies G ij pertaining to certain site exchange reactions occurring between cations are used as the models parameters. For a fully normal spinel, for example, G AB = G o (AB 2 O 4 ), is the (measurable) Gibbs energy of pure normal AB 2 O 4 which can be used directly as an optimized parameter. The Gibbs energy of site exchange reactions between cations in the tetrahedral and octahedral sites are the model parameters and are denoted by Δ and I parameter. Gibbs energies Δ AB of following site exchange reaction is given by AB + BA = AA + BB (2.36) Δ AB = G AA + G BB G AB G BA (2.37) which is used as model parameters. O Neill and Navrotsky [12] found out that the Δ AB should have the value of about 40kJ/mol. Gibbs energies I AB of following site exchange reaction is given by 2AB = AB + BA (2.38) I AB = G AB + G BA 2G AB (2.39) which are indicators of tendency of spinel towards the formation of an inverse spinel structure and this model parameter helps in optimizing the cation distribution data. The present system is a concern as the spinel contains Mn. Mn has three valence states in spinel, Mn 2+, Mn 3+ and Mn 4+. Therefore, the structure of the spinel solution and their Gibbs energy formula is more complex. This will be explaining in detail in Chapter 4. 27

29 2.3. References [1] A.D. Pelton, M. Blander, Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach application to silicate slags, Metall. Mater Trans. B, 17B, (1986). [2] A.D. Pelton, S.A. Degterov, G. Eriksson, C. Robelin, Y. Dessureault, The modified quasichemical model. I. Binary solutions, Metall. Mater. Trans. B, 31B, (2000). [3] B.E. Warren and J. Biscoe, Fourier analysis of x-ray patterns of soda-silica glass, J. Am. Ceram. Soc., 21, (1938). [4] A.D. Pelton, A general "geometric" thermodynamic model for multicomponent solutions, CALPHAD, 25(2), (2001). [5] Patrice Chartrand and Arthur D. Pelton, On the Choice of Geometric Thermodynamic Models, J. Phase Equilib., 21, (2000). [6] [7] I-H Jung, S.A. Decterov, and A.D. Pelton, Critical thermodynamic evaluation and optimization of the MgO-Al2O 3, CaO-MgO-Al 2 O 3 and MgO-Al 2 O 3 -SiO 2, J. Phase Equilib. Diffus., 25(4), (2004). [8] S.A. Degterov, E. Jak, P.C. Hayes, A.D. Pelton, Experimental study of phase equilibria and thermodynamic optimization of the Fe Zn O system, Metall. Mater. Trans. B. 32B, (2001). [9] M. Hillert, B. Jansson and B. Sundman, Application of the Compound-Energy Model to Oxide Systems, Z. Metallkd., 79, (1988). [10] O. Redlich and A.T. Kister, Algebraic representation of thermodynamic properties and the classification of solutions, Industrial and Engineering Chemistry, 40[2], (1948). [11] A.D. Pelton and M. Blander, Thermodynamic analysis of ordered liquid solutions by a modified quasichemical approach - application to silicate slags, Metall. Mater Trans. B, 17B, (1986). [12] H.S.C. O Neill and A. Navrotsky, Cation distributions and thermodynamic properties of binary spinel solid solutions, Am. Mineral., 69, (1984). 28

30 3. Method of Operation The objective of the present work was to prepare a critically evaluated thermodynamic database for Ca-Mg-Mn-O system. All the calculations and optimizations in the present work were performed with the FactSage TM thermochemical software. The various steps followed in the present work which collectively come under the CALPHAD approach were: (i) Identification of the binary system to be optimized. (ii) Collection of data in the literature for the system: Thermodynamic data: includes phase equilibria (phase diagrams, two- ог three-phase equilibria among solids/1iquid/gas), calorimetric data (heat capacity, enthalpy of formation and enthalpy of mixing), enthalpy of formation for compounds, vapour pressures (Кnudsen сеll, Langmuir method), chemical potentials (emf), activities of constituents in a solution, etc. Structural data: includes cation distributions between sublattices, lattice parameters, etc. Physical properties such as magnetism, electrical conductivity, etc. may sometimes help in the evaluation of the system. If very few experimental data are available which are not sufficient to define the thermodynamic properties of the system, useful data from а higher-order system of which the system of interest is а sub-system can be used. (iii) Selection of the appropriate thermodynamic model: An appropriate thermodynamic model representing the Gibbs energy functions for a phase is required. For that, a good physical model based on the structure of the phase is selected which increases the accuracy of predictions of solution properties of multicomponent systems from lower order (binary + ternary) model parameters. (iv) Critical evaluation of collected experimental data: The literature data which includes all experimental data must be evaluated before doing the optimization. The experimental data by different authors were often found to differ from each other by more than the stated experimental error limits. Sometimes experimental data for a 29

31 particular system were not thermodynamically consistent with each other. Therefore, all the available experimental data were evaluated on the basis of experimental techniques, sample preparation and thermodynamic consistency. Sometimes, the accuracy of the experimental data was difficult to evaluate from the description of the experimental technique, then their consistency or inconsistency was judged during the optimization of the entire system. Moreover, the accuracy of the experimental data in lower-order systems can be evaluated from the data in higher-order systems by extrapolation. All possible experimental errors should be considered during the evaluation and optimization of a system. (v) Optimization of model parameters for a system: After evaluation of the experimental data, the next step is optimization which was performed on the basis of selected reliable data to obtain the values of the model parameters. (vi) Back calculation of all thermodynamic data and phase diagrams: Once satisfactory model parameters were obtained, all the thermodynamic data and experimental data were back-calculated from the thermodynamic models for comparing with the optimized values. The FactSage TM (FactSage 6.3) thermochemical software was used to perform all calculations for a particular system. (vii) Evaluation of ternary systems: To estimate the Gibbs energies of solutions in the ternary systems, the obtained model parameters for the binary sub-systems were combined with previously optimized binary parameters of the other binary sub-systems. By doing this, evaluations and predictions were made for the ternary systems. 30

32 4. Critical evaluation and thermodynamic modelling of the Mg-Mn-O system 4.1. Introduction The magnesium-manganese oxide is of great interest in metallurgical fields (iron and steel making, high manganese steel production) since the manganese plays an important role as a major alloying element in steel. Therefore, the knowledge for the manganese oxide containing system is valuable to the industries. In this regard, a research on the thermodynamic properties and phase equilibria in the Mg-Mn-O is necessary. In this system Mg-Mn-O, spinel phases (cubic and tetragonal) is of interest in the view of thermodynamic modeling because there are couples of things to be considered (ex., valencies of Mn, cation distribution on tetrahedral and octahedral sites). Despite its importance, the phase equilibria in this system have not been well studied. Experimental study of the system is complicated by the strong dependence of the equilibria on the oxygen pressure and by the high melting temperature of the spinel phase. Therefore, critical assessment of the data is required in order to understand and model this system more accurately. The present study is a part of a complete database development of the CaO-Fe t O-SiO 2 -MgO-MnO-Na 2 O-Al 2 O 3 -P 2 O 5 -CaF 2 system for application in the steel industries. All the thermodynamic calculations in the present study were performed with the FactSage [1] software Phases and thermodynamic models The calculated phase diagram of the Mg-Mn-O system at 1000 C and 1 bar total pressure is presented in Figure 4.1. The following solution phases are found in the MgO-MnO-Mn 2 O 3 system: (i) Slag (molten oxide phase): MgO-MnO-MnO 1.5 (ii) Monoxide (periclase): MgO-MnO-MnO 1.5 (iii) Cubic spinel (encompassing cubic-mgmn 2 O 4, cubic-mn 3 O 4 ): (Mg 2,Mn 2 ) T Mg 2,Mn 2, Mn 3,Mn 4, a 2 O O4 (iv) Tetragonal spinel (encompassing tetragonal Mn 3 O 4 ): (Mg 2,Mn 2,Mn 3 ) T Mg 2,Mn 2, Mn 3, a 2 O O 4 31

33 (v) Mg 6 MnO 8 : built from the existing MgO and MnO 2 from FToxide database. Cations shown within a set of brackets for spinel occupy the same sublattice. T and O represent the tetrahedral and octahedral cationic sites in spinel, respectively Molten oxide (slag) The modified quasichemical model [2-5], which takes into account short-range ordering of second-nearest-neighbor cations in the ionic melt, is used for modeling the slag. For example, for the MgO-MnO-MnO 1.5 slag these reactions are: (A A) + (B B) = 2(A B) (4.1) where A and B are Mg 2+, Mn 2+ and Mn 3+, and (A B) represents a second-nearest-neighbour A- B pair. Gibbs energies of these above reaction g A are the parameters of the model which may be expanded as empirical functions of composition. The Gibbs energy of the solution is given in Eq The component of the slag is taken as MgO-MnO-MnO 1.5. Although Mn can have higher oxidation states, only the divalent and trivalent oxidation states, which predominate at oxygen partial pressures less than 1.0 bar, are considered in the present study. The components are written as MnO 1.5 rather than Mn 2 O 3 simply to indicate that Mn 3+ ions are distributed as independent particles between oxygen in the liquid solution and not as ion pairs. The binary sub-systems MnO-MnO 1.5 [6] and MgO-MnO [7] has already been critically evaluated and optimized and the optimized model parameters are used as the basis of the present study. All second-nearest-neighbor coordination numbers used in the present model for the slag are the same as in previous studies. The binary sub-system MgO-MnO 1.5 has been optimized in the present studies which are listed in Table 4.1. The properties of the ternary MgO-MnO-MnO 1.5 slag solution were calculated from the binary parameters using a symmetric Kohler-like approximation [8] which assumes that the energy of reaction (4.1) remains constant as MnO 1.5 is added to an MgO-MnO solution at constant MgO/MnO ratio, and similarly for addition of MnO to MgO-MnO 1.5 solutions and of MgO to MnO-MnO 1.5 solutions. No ternary interaction parameters are needed. 32

34 Monoxide solution Monoxide solution has rock-salt structure. It was modeled as a simple random mixture of all cations, Mg 2+, Mn 2+, and Mn 3+ ions on cation sites using a simple polynomial excess Gibbs energy terms [8]. It is assumed that cation vacancies remain associated with Mn 3+ to maintain electrical neutrality and so do not contribute to the configurational entropy. The Gibbs energy per mole of the solution is expressed as follow: G m i G i o i RT i ln i i i ( i m i i ) ( n ) mn ex q i g ternary i (4.6) where is the Gibbs energy of component like MgO, MnO and MnO 1.5 and is mole fraction mn of component. The binary parameter q i of MgO-MnO and MgO-MnO 1.5 system was optimized mn in the present study as described in the following section. These are listed in Table 4.1. q i of MnO-MnO 1.5 was optimized previously [6]. The properties of ternary monoxide MgO-MnO- MnO 1.5 were calculated from the binary parameters with asymmetric Kohler-like approximation [8]. No ternary excess parameter was used in the present study Spinel: cubic and tetragonal Tetrahedral and octahedral sites are the two distinct cationic sites of spinel. Thus, cationic distribution between these two sublattices is important for determining the physical and thermodynamic properties of spinel. There are two types of spinel phases in the Mg-Mn-O system: cubic and tetragonal spinels. Grundy et al. [9] observed that pure Mn 3 O 4 has tetragonal spinel structure and it transforms to cubic spinel over 1172 C in air. The ionic configuration of both tetragonal and cubic Mn 3 O 4 spinel was found out by Dorris and Mason [10] from their electrochemical seebeck experimental technique. This structural information was properly implemented in the development of the present thermodynamic models for the cubic and tetragonal spinel phases in the Mg-Mn-O system. For both the spinel solution, a two sublattice spinel model [11] has been developed within the framework of the compound energy formalism (CEF) [12]. It has earlier been explained in Section

35 Certain linear combinations of the G ij parameters (Δ) having physical significance is used as the optimized model parameters as shown in Table 4.1. The physical significance of these linear combinations (Δ) is already been discussed 13] which are related to the energies of classical site exchange reactions. By doing this, the model parameters could have certain physical meaning which helps in completing the thermodynamic modeling than individually giving a value to the G ij parameters without any particular reason. Moreover, it helps in increasing the predictive ability of the model. Details of the linear combinations of G ij parameters for both cubic and tetragonal spinels are given in Table 4.1. Here, B, J, K, L and V stands for Mg 2+,Mn 2+, Mn 3+, Mn 4+ and Vacancy, respectively Cubic spinel Cubic spinel has (Mg 2,Mn 2 ) T Mg 2,Mn 2,Mn 3,Mn 4 O, a O4 2 structure including vacancy (Va) on octahedral site. 10 end-member Gibbs energies are required for the model. Among them, four end members Gibbs energies (G JJ, G JK, G JL and G JV ) were already fixed from the Mn-O system (Mn 3 O 4 ) [6] and two more (G BB and G BV ) were fixed in the optimization of the Mg-Al-O spinel solution [14]. Optimized values of the four remaining parameters (G BK, G BJ, G BL and G JB ) were obtained in the present study as described in the following sections. Physically meaningful combinations of G ij for the cubic spinel are listed in Table 4.1. These are the model parameters which are optimized in the present study. There are 4 model parameters which consist of 3 Δ parameters along with the Gibbs energy of stoichiometric spinel MgMn 2 O 4 as one parameter. As, two of the Δ parameter (, ) has same effect on the Mn rich side, therefore, one Δ parameter ( ) is set to zero and another Δ parameters ( along with the Gibbs energy of stoichiometric spinel MgMn 2 O 4 parameter is used to optimize the available experimental data. The fourth parameter ( ) was optimized to determine the cation distribution of MgMn 2 O 4. The values of all the model parameters are given in Table 4.1. Due to Jahn-Teller distortion [15], the cubic MgMn 2 O 4 show the slightly distorted tetragonal structure. However, it is different from standard tetragonal spinel structure like tetragonal Mn 3 O 4 spinel. From the thermodynamic viewpoint, Jahn-Teller distortion is not the first order transition 34

36 as there is no sudden change in lattice parameters with temperature [16].Thus, in the present study, the distorted tetragonal structured spinel was treated as extension of cubic spinel Tetragonal spinel Tetragonal spinel has (Mg 2,Mn 2,Mn 3 ) T Mg 2,Mn 2,Mn 3 O, a O4 2 structure including vacancy (Va) on octahedral sites. Like cubic spinel, 12 end-member Gibbs energies are required for the model. Among them, 8 end member Gibbs energies were already determined from the Mn-O [6] and Mg-Al-O [14]. 4 other Gibbs energies were determined in the present study. The model parameters are presented in Table Stoichiometric compound Mg 6 MnO 8, Mn 2 O 3 and MnO 2 were treated as stoichiometric compound Metallic phases All metallic phases (CBCC, CUB, FCC, BCC and Liquid) were treated as simple substitutional solutions and their Gibbs energy of mixing were taken from FSstel database [17]. Table 4.1: Optimized model parameters of solutions in the MgO-MnO-Mn 2 O 3 system Cubic Spinel: G BK = G o (cubic-mgmn 2 O 4 ) = G o (MgO) + G o (Mn 2 O 3 ) ΔS f = J/mol-K) ΔH f - TΔS f (ΔH f = J/mol and o H 298 = J/mol o S 298 = J/mol K C p = T T T T T -3 (298K < T < 320K); T T T T T -3 (320K < T < 1161K); T T T -3 (1161K < T < K); ( K < T < 3050K) Δ BJ:JK = G BJ + G JK G JJ G BK = 0 35